Plotting a 4D graph with the fourth dimension using color (a 3D graph with the fourth dimension represented using colors)

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Bas123
Bas123 2023-1-15
编辑： Bas123 2023-1-17
I would like to know how to plot R0 (basic reproduction number of a disease) against three given parameters on a 3D plot where the x-, y-, and z- axes represent the three parameters and a color scheme represents R0. So, the graph should essentially be a 3D plot, but the fourth dimension (depicting R0) should be in terms of a color scheme.
In the current example, I wish to plot R0 against the three parameters beta, p, and phi which could all vary between 0 and 1. The formula for R0 and the parameters are given below.
c = 0.01;
%beta = 0.4;
gamma = 0.2;
theta = 0.2778;
%p = 0.05;
%phi = 0.95;
epsilon = 0.084;
delta = 0.011;
mu = 0.000027;
R0 = (epsilon*c*beta*theta*(mu+(1-phi)*p))/(mu*(mu+p)*(mu+epsilon)*(mu+gamma+delta))
I would highly appreciate if someone could help me on this. Thanks a lot in advance!

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回答（1 个）

Torsten
Torsten 2023-1-15
编辑：Torsten 2023-1-15
Use "slice".
This will display R0 on predefined planes in 3d space.
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Bas123
Bas123 2023-1-17
Hi again, thanks for the great question. Yes, you're right. I am not sure if I was using accurate terminology when I made it look like R0 values as high as 450 are "epidemiologically meaningless" because any non-negative value of R0 is theoretically possible. That said, there might be a problem with the model when it gives such large values for R0. However, I don't think that there is anything erroneous with my model or the parameter values to the best of my knowledge, on which I might well be wrong as well. In fact, none of the other simulations that I did pertaining to R0 gave results like these. So, I drew similar plots of R0 for three other models that I found in the literature and examined what those graphs look like. Surprisingly, those plots also produced substantially large values for R0 as mine did. I was hence wondering if there are issues with those models as well or if this is a typical phenomenon. May be they didn't figure it out as they didn't go about producing a graph like this, nor did I until I came up with the current graph. Therefore, I believe that this is a question which is worthy of a discussion on its own, perhaps on a separate platform. Thanks for all your inputs.
Bas123
Bas123 2023-1-17
编辑：Bas123 2023-1-17
Another thought that just came to my mind is that we are mainly concerned not so much about the actual value/s of R0 as the behavior of the parameters of interest at/near the threshold R0=1. So, restricting R0 on a smaller interval like [0,2] or [0,5] would help us get a better sense of (closer look at) how the three parameters affect R0 near the threshold (which, in fact, is the purpose of such a graph). If the graph was based on data, then truncating a part of it would certainly constitute an act of cheating, but a case like this, in my opinion, doesn't seem to do so.

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